Log-log plots of iteration steps required to reach convergence versus total number of grid points (grid volume). In the case of the PMG method, “effective” iteration steps are used. This is computed as the sum of iteration steps at each grid level divided by the scaling factor of that grid level relative to the finest grid level, e.g. factors of 1, 8, 64, and 512, respectively. Top Left: PICCG, Top Right: PCG, Bottom Left: 4 Level V-Cycle PMG with SOR/Gauss-Siedel Relaxation, Bottom Right: PSOR.